AlgebraIdeals¶

class
sage.categories.algebra_ideals.
AlgebraIdeals
(A)¶ Bases:
sage.categories.category_types.Category_ideal
The category of twosided ideals in a fixed algebra \(A\).
EXAMPLES:
sage: AlgebraIdeals(QQ['a']) Category of algebra ideals in Univariate Polynomial Ring in a over Rational Field
Todo
 Add support for non commutative rings (this is currently not
supported by the subcategory
AlgebraModules
).  Make
AlgebraIdeals(R)
, returnCommutativeAlgebraIdeals(R)
whenR
is commutative.  If useful, implement
AlgebraLeftIdeals
andAlgebraRightIdeals
of whichAlgebraIdeals
would be a subcategory.

algebra
()¶ EXAMPLES:
sage: AlgebraIdeals(QQ['x']).algebra() Univariate Polynomial Ring in x over Rational Field

super_categories
()¶ The category of algebra modules should be a super category of this category.
However, since algebra modules are currently only available over commutative rings, we have to omit it if our ring is noncommutative.
EXAMPLES:
sage: AlgebraIdeals(QQ['x']).super_categories() [Category of algebra modules over Univariate Polynomial Ring in x over Rational Field] sage: C = AlgebraIdeals(FreeAlgebra(QQ,2,'a,b')) sage: C.super_categories() []
 Add support for non commutative rings (this is currently not
supported by the subcategory